OpenGL移动对象并保持变换 [英] OpenGL move object and keep transformation
问题描述
我有一个物体，它是变形的(在 Y 轴上旋转 45 度).目标是在 x 和 y 轴上移动(平移)对象并保持变换效果不变.很难解释，所以我拍了一张:
I've a object, which is transfomred (rotated at 45deg on the Y axis).
The target is to move (translate) the object on the x and y axis and keep the transformation effect as it is.
Its very hard to explain, so I made a picture:
我知道 opengl 中相机的概念，我知道我不能真正移动相机，但实际上一切都在相机周围移动.有人真的知道如何实现这一目标吗?
I know the concept of the camera in opengl and i know i cant really move the camera but in fact everything is moving around the camera. Does someone actually know how to achieve this?
我的代码:
//set mvp
matrixProj = new PerspectiveProjectionMatrix(fovy, aspect, near, far);
matrixView = new ModelMatrix();
matrixView.LookAtTarget(new Vertex3f(0, 0, 2), new Vertex3f(0, 0, 0), new Vertex3f(0, 1, 0));
matrixModel = new ModelMatrix();
matrixModel.SetIdentity();
matrixModel.RotateY(45);
matrixModel.Translate(-2, -2, 0);
Matrix4x4 mvp = matrixProj * matrixView * matrixModel;
Gl.UniformMatrix4(Gl.GetUniformLocation(shaderProgram, "MVP"), 1, false, mvp.ToArray());
//draw quad
Gl.Begin(PrimitiveType.Quads);
Gl.Vertex3(-2, 2, 0);
Gl.Vertex3(2, 2, 0);
Gl.Vertex3(2, -2, 0);
Gl.Vertex3(-2, -2, 0);
Gl.End();
推荐答案
您必须更改说明的顺序.通过将对象的平移矩阵乘以旋转矩阵来执行围绕对象轴的旋转.这意味着您必须先进行平移，然后再进行旋转.
You have to change the order of the instructions. A rotation around the axis of the object is performed, by multiplying the translation matrix of the object by the rotation matrix. This means you have to do the translation first and then the rotation.
matrixModel = new ModelMatrix();
matrixModel.SetIdentity();
matrixModel.Translate(-2, -2, 0);
matrixModel.RotateY(45);
注意，翻译矩阵如下所示:
Note, the translation matrix looks like this:
Matrix4x4 translate;
translate[0] : ( 1, 0, 0, 0 )
translate[1] : ( 0, 1, 0, 0 )
translate[2] : ( 0, 0, 1, 0 )
translate[3] : ( tx, ty, tz, 1 )
围绕 Y 轴的旋转矩阵如下所示:
And the rotation matrix around Y-Axis looks like this:
Matrix4x4 rotate;
float angle;
rotate[0] : ( cos(angle), 0, sin(angle), 0 )
rotate[1] : ( 0, 1, 0, 0 )
rotate[2] : ( -sin(angle), 0, cos(angle), 0 )
rotate[3] : ( 0, 0, 0, 1 )
矩阵乘法的工作原理如下:
A matrix multiplication works like this:
Matrix4x4 A, B, C;
// C = A * B
for ( int k = 0; k < 4; ++ k )
for ( int l = 0; l < 4; ++ l )
C[k][l] = A[0][l] * B[k][0] + A[1][l] * B[k][1] + A[2][l] * B[k][2] + A[3][l] * B[k][3];
translate *rotate 的结果是这样的:
model[0] : ( cos(angle), 0, sin(angle), 0 )
model[1] : ( 0, 1, 0, 0 )
model[2] : ( -sin(angle), 0, cos(angle), 0 )
model[3] : ( tx, ty, tz, 1 )
注意，rotate * translate 的结果是:
model[0] : ( cos(angle), 0, sin(angle), 0 )
model[1] : ( 0, 1, 0, 0 )
model[2] : ( -sin(angle), 0, cos(angle), 0 )
model[3] : ( cos(angle)*tx - sin(angle)*tx, ty, sin(angle)*tz + cos(angle)*tz, 1 )
透视投影矩阵如下所示:
A perspective projection matrix looks like this:
r = right, l = left, b = bottom, t = top, n = near, f = far
2*n/(r-l) 0 0 0
0 2*n/(t-b) 0 0
(r+l)/(r-l) (t+b)/(t-b) -(f+n)/(f-n) -1
0 0 -2*f*n/(f-n) 0
哪里:
r = w / h
ta = tan( fov_y / 2 );
2*n / (r-l) = 1 / (ta*a) ---> 1/(r-l) = 1/(ta*a) * 1/(2*n)
2*n / (t-b) = 1 / ta ---> 1/(t-b) = 1/ta * 1/(2*n)
如果你想用一个偏移量(x, y)取代视野，那么你必须这样做:
If you want to displace the filed of view by an offset (x, y), then you have to do it like this:
x_disp = 1/(ta*a) * x/(2*n)
y_disp = 1/ta * y/(2*n)
1/(ta*a) 0 0 0
0 1/t 0 0
x_disp y_disp -(f+n)/(f-n) -1
0 0 - 2*f*n/(f-n) 0
像这样设置透视投影矩阵:
Set up the perspective projection matrix like this:
float x = ...;
float y = ...;
matrixProj = new PerspectiveProjectionMatrix(fovy, aspect, near, far);
matrixProj[2][0] = x * matrixProj[0][0] / (2.0 * near);
matrixProj[2][1] = y * matrixProj[1][1] / (2.0 * near);
对于 glFrustum，像素偏移可以这样应用:
To glFrustum, a pixel offset, can be applied like this:
float x_pixel = .....;
float y_pixel = .....;
float x_dipl = (right - left) * x_pixel / width_pixel;
float y_dipl = (top - bottom) * y_pixel / height_pixel;
glFrustum( left + x_dipl, right + x_dipl, top + y_dipl, bottom + y_dipl, near, far);
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